The AJ conjecture for knots

Let $K$ be a knot in $S^3$. Let $A(K)(L,M)$ denote its $A$-polynomial, and let $A_q(K)$ denote the $A_q$-polynomial of the recursion ideal of its colored Jones function. Under the identification of the geometric variables $(L,M^2)$ with the basic operator variables $(E,Q)$, write the quantum polynomial as $A_q(K)(L,M^2)$. AJ conjecture. For every knot in $S^3$,

$$A(K)(L,M)=\epsilon A_q(K)(L,M^2).$$

This conjecture asserts that the classical $A$-polynomial is obtained from the quantum recursion polynomial after specialization, up to the normalization factor represented by $\epsilon$. It connects the colored Jones polynomial's $q$-difference recursion with the character variety of the knot complement.